The 31-year-old, who made 35 appearances for the Trotters last season, had his contract at the Reebok cancelled and dropped down a division to be reunited with Kenny Jackett, who signed him for Swansea 10 years ago.
"I'm excited at what is a great opportunity," Ricketts told the club's official website. "I know Kenny from working under him at Swansea and I know what a big club this is with huge support.
"Dropping down a division doesn't put me off at all, because of the size of the club. Wolves are not a club looking to stay in League One - we are looking forward and looking upwards.
"Kenny signed me from Telford and I had two great years at Swansea with him where we got promoted the first year and narrowly missed out the second. I know what he is all about and I trust him."
Ricketts will be playing alongside Wales team-mates Wayne Hennessey and David Edwards as Wolves look for an immediate return to the second tier.
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